As I have said before...
Apples and oranges really...
Atmosphere (for best homebrew support - playing backups isnt very high on the agenda). All/most modules have been rewritten / reimplemented to make the system truely more open. Playing backup games is a byproduct of this development. Not the aim.
SXOS is great if you need something that just works. Most of the time. XCI support is JUST for playing backups. They have an installer too, which seems to work OK for the most part. Homebrew is not well supported and SXOS is frowned upon by devs. However, if you have young children who are always losing cartridges - SXOS can be a godsend.
Nutshell:
If you are computer illiterate and want to "chip" your Switch to play backups, use SXOS. It is very easy to use. Forget about any serious developing. It is considered the ba$tard child of the Switch scene. Even though it does what it says on the tin.
If you aren`t frightened of computers, like to tinker, maybe run emulators etc with the best support and play the odd backup, then Atmosphere is for you.
Both have emuNAND solutions, both play backups, both involve cost (Atmosphere - time and little knowledge, SXOS, actual money)
We use both in this house. For different jobs. SXOS as I am sick of replacing Mario Odyssey and Mario Kart / Minecraft, and Atmosphere for N64 and devving (we do a bit here).
Long term... As Atmosphere is completely open-sores, it is likely to be supported in the months and years ahead. TX have demo`d SXOS running on a Switch lite. However, you are at the mercy of just a few TX devs. Regarding the Switch Lite - It is possible to run Atmosphere on it too... Trust me on this. Details will come soon...
Depends what you want it for. Get both... They are both very good and they are BOTH the reason we have such a thriving scene, not seen since the Amiga days... Fit a SAMD modchip and you are at the races.